Atkin-Lehner |
3+ 11+ 17+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
31977c |
Isogeny class |
Conductor |
31977 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
24192 |
Modular degree for the optimal curve |
Δ |
22588584777 = 39 · 11 · 172 · 192 |
Discriminant |
Eigenvalues |
-1 3+ -2 2 11+ 6 17+ 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-2081,-35288] |
[a1,a2,a3,a4,a6] |
j |
50611941099/1147619 |
j-invariant |
L |
1.4157199706403 |
L(r)(E,1)/r! |
Ω |
0.70785998532096 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
31977f1 |
Quadratic twists by: -3 |